The present invention relates to method and apparatus for making a diaper and a new diaper construction. U.S. Pat. No. 3,860,003 discloses a diaper construction with elastic strips adhesively secured to the backing sheet of a diaper to provide a close fit of the diaper to the baby's legs. The elastic ribbon provides elastically contractable leg openings. U.S. Pat. No. 4,081,301 discloses apparatus for making diapers of the type disclosed in U.S. Pat. No. 3,860,003. In a diaper construction of the type exemplified by U.S. Pat. No. 3,860,003, it is desirable that the elastic be only in the leg-contacting diaper portions rather than in the waistband portions. Accordingly, the elastic band is only adhered to the facing or backing sheet in the leg-contacting zone of the diaper. To accomplish this result, glue is intermittently applied to the continuously fed elastic band so that it will adhere to the desired leg-contacting portion of the diaper but not the waistband portions of the diaper. Inasmuch as the elastic bands are superimposed on the backing as a continuous ribbon, the bands extend to the ends of the diaper. When the diapers are cut from the web, the tension on the non-glued portions of the elastic bands adjacent the cuts is relaxed and the ends of the bands contract. The non-adhering portions of the elastic ribbon provide or serve no useful function in the completed diaper and constitute considerable waste of ribbon. The wasted portion of the ribbon can constitute as much as 40% of the total length of ribbon used per diaper.